Algebraic flux correction III. Incompressible flow problems

Algebraic FEM-FCT and FEM-TVD schemes are integrated into incompressible flow solvers based on the 'Multilevel Pressure Schur Complement' (MPSC) approach. It is shown that algebraic flux correction is feasible for nonconforming (rotated bilinear) finite element approximations on unstructured meshes. Both (approximate) operator-splitting and fully coupled solution strategies are introduced for the discretized Navier-Stokes equations. The need for development of robust and efficient iterative solvers (outer Newton-like schemes, linear multigrid techniques: optimal smoothers/preconditioners) for implicit high-resolution schemes is emphasized. Numerical treatment of extensions (Boussinesq approximation, k-epsilon turbulence model) is addressed and pertinent implementation details are given. Simulation results are presented for three-dimensional benchmark problems as well as for prototypical applications including multiphase and granular flows.